FBN环上模范畴的子范畴分类

Classifications of the Subcategories of Modules over FBN Rings

将模的support,Spec(R)的coherent子集等概念推广到非交换诺特环的情形.利用不可分内射模的结构,由模的相关素理想及support分别导出R-模范畴的全子范畴与Spec(R)的子集之间的一些对应关系.由相关素理想对应导出{Mod-R的对子模、扩张、直接并封闭的全子范畴}与{Spec(R)的子集}是一一对应的充要条件,通过取模的support导出{Mod-R的对直和封闭的thick子范畴}与{Spec(R)的coherent子集}是一一对应的一个充分条件.

The notions such as support of modules and coherent subsets of Spec（R） are generalized to noncommutative noetherian rings. And by investigating the structure of indecomposable injective modules, some maps between subcategories of Mod-R and subsets of Spec（R） by taking associated prime ideas and support of modules over FBN rings are gained. For the former, the ring when there is a bijection between the set of full subcategories of ModR, which are closed under taking submodules, extensions, and direct unions, and the set of subsets of Spec（R） is characterized. While for the latter, a suficient condition to insure there is a bijection between the set of full subcategories of Mod R, which are thick and closed under taking direct sums, and the set of coherent subsets of Spec（R） is given.